2013
11-10

# Georgia and Bob

Georgia and Bob decide to play a self-invented game. They draw a row of grids on paper, number the grids from left to right by 1, 2, 3, …, and place N chessmen on different grids, as shown in the following figure for example:

Georgia and Bob move the chessmen in turn. Every time a player will choose a chessman, and move it to the left without going over any other chessmen or across the left edge. The player can freely choose number of steps the chessman moves, with the constraint that the chessman must be moved at least ONE step and one grid can at most contains ONE single chessman. The player who cannot make a move loses the game.

Georgia always plays first since “Lady first”. Suppose that Georgia and Bob both do their best in the game, i.e., if one of them knows a way to win the game, he or she will be able to carry it out.

Given the initial positions of the n chessmen, can you predict who will finally win the game?

The first line of the input contains a single integer T (1 <= T <= 20), the number of test cases. Then T cases follow. Each test case contains two lines. The first line consists of one integer N (1 <= N <= 1000), indicating the number of chessmen. The second line contains N different integers P1, P2 ... Pn (1 <= Pi <= 10000), which are the initial positions of the n chessmen.

For each test case, prints a single line, “Georgia will win”, if Georgia will win the game; “Bob will win”, if Bob will win the game; otherwise ‘Not sure’.

2
3
1 2 3
8
1 5 6 7 9 12 14 17


Bob will win
Georgia will win


/* @author: */
import java.util.Scanner;
import java.util.Arrays;
public class Main{
public static void  main(String args[] ){
int arr[]=new int[10005];
Scanner sc=new Scanner(System.in);

int T=sc.nextInt();

while((T--)!=0){
int n=sc.nextInt();
arr[0] = 0;
for (int i = 1; i <= n;i++)
arr[i]=sc.nextInt();
Arrays.sort(arr,1,n + 1);
int ans = 0;
for (int i = n; i >= 1; i -= 2)
ans ^= arr[i] - arr[i-1] - 1;
if (ans==0) System.out.printf ("Bob will win\n");
else System.out.printf ("Georgia will win\n");
}
}
}

1. 约瑟夫也用说这么长……很成熟的一个问题了，分治的方法解起来o(n)就可以了，有兴趣可以看看具体数学的第一章，关于约瑟夫问题推导出了一系列的结论，很漂亮

2. 学算法中的数据结构学到一定程度会乐此不疲的，比如其中的2－3树，类似的红黑树，我甚至可以自己写个逻辑文件系统结构来。

3. 有一点问题。。后面动态规划的程序中
int dp[n+1][W+1];
会报错 提示表达式必须含有常量值。该怎么修改呢。。